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Path Dependent Option Pricing: the path integral partial averaging method

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  • Andrew Matacz

    (Science & Finance)

Abstract

In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium term options it leads to a general approximation formula that only requires the evaluation of a one dimensional integral. I illustrate the application of the method to Asian options and occupation time derivatives.

Suggested Citation

  • Andrew Matacz, 2000. "Path Dependent Option Pricing: the path integral partial averaging method," Papers cond-mat/0005319, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0005319
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    References listed on IDEAS

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    1. Vadim Linetsky, "undated". "Occupation Time Derivatives," Computing in Economics and Finance 1997 103, Society for Computational Economics.
    2. Carl Chiarella & Nadima El-Hassan, 1997. "Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques," Working Paper Series 72, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    3. Carl Chiarella & Nadima El-Hassan & Adam Kucera, 2004. "Evaluation of Point Barrier Options in a Path Integral Framework Using Fourier-Hermite Expansions," Research Paper Series 126, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Chiarella, Carl & El-Hassan, Nadima & Kucera, Adam, 1999. "Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1387-1424, September.
    5. Eydeland, A, 1994. "A Fast Algorithm for Computing Integrals in Function Spaces: Financial Applications," Computational Economics, Springer;Society for Computational Economics, vol. 7(4), pages 277-285.
    6. Linetsky, Vadim, 1998. "The Path Integral Approach to Financial Modeling and Options Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 129-163, April.
    7. Eleonora Bennati & Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach To Derivative Security Pricing I: Formalism And Analytical Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 381-407.
    8. Carl Chiarella, Nadima El-Hassan, & Adam Kucera, "undated". "Option Pricing in a Path Integral Framework Using Fourier-Hermite Series Expansions," Computing in Economics and Finance 1997 132, Society for Computational Economics.
    9. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods," Papers cond-mat/9901279, arXiv.org.
    10. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
    11. Robert Jarrow, 2017. "Derivatives," World Scientific Book Chapters, in: THE ECONOMIC FOUNDATIONS OF RISK MANAGEMENT Theory, Practice, and Applications, chapter 3, pages 19-28, World Scientific Publishing Co. Pte. Ltd..
    12. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results," Papers cond-mat/9901277, arXiv.org.
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    Cited by:

    1. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    2. Luca Capriotti, 2006. "The Exponent Expansion: An Effective Approximation Of Transition Probabilities Of Diffusion Processes And Pricing Kernels Of Financial Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1179-1199.
    3. G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2006. "Pricing exotic options in a path integral approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 55-66.
    4. G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2004. "Pricing Exotic Options in a Path Integral Approach," Papers cond-mat/0407321, arXiv.org, revised May 2006.

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